Unitary scalar multiplet current ($j_T^{\mu }=i[({\partial }^{\mu }{\Phi }^{†})T\Phi -{\Phi }^{†}T{\partial }^{\mu }\Phi ]$)

For a complex scalar field multiplet with canonical kinetic term and scalar potential invariant under $\Phi \mapsto e^{i\epsilon T}\Phi$, a constant Hermitian matrix $T$ gives the displayed Noether current. Vary the field and its conjugate independently in the Noether current for a first-derivative scalar field. A common alternative convention reverses both the parameter and current sign. Its divergence vanishes on shell.